Apart from the above mentioned papers [1]}, [2]}, also the papers
[3]}, [4]}, [5]} deal with the knapsack and subset sum problem for groups.
In [3]} the authors study the effect of free and direct product constructions on the complexity
of the subset sum and knapsack problem. In [5]} the authors proved that knapsack is undecidable
for the direct product of sufficiently many copies of the discrete Heisenberg group (this direct product is nilpotent
of class 2). On the other hand, knapsack is shown to be decidable for the discrete Heisenberg group, which implies
that decidability of knapsack is not preserved by direct products. Moreover, it is shown in [5]} that
knapsack is decidable for every co-context-free group and that there exist polycyclic groups with an NP-complete
subset sum problem.
Using the results of [5]}, Godin proved in [4]} that there are automaton groups
with an undecidable knapsack problem. On the other hand for so called bounded automaton groups,
Godin proved decidability of the knapsack problem. The class of bounded automaton groups includes
important groups like for instance Grigorchuk's group, Gupta-Sidki groups, and the Basilica group.
